Precalculus Examples

$\frac{x^{2} + 14 + 45}{x^{2} - 25}$

Step 1

Add $14$ and $45$ .

$\frac{x^{2} + 59}{x^{2} - 25}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $25$ as $5^{2}$ .

$\frac{x^{2} + 59}{x^{2} - 5^{2}}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 5$ .

$\frac{x^{2} + 59}{(x + 5) (x - 5)}$